The Six and Eight-Vertex Models Revisited

Elliott Lieb's ice-type models opened up the whole field of solvable models in statistical mechanics. Here we discuss the “commuting transfer matrix” T,Qequations for these models, writing them in a more explicit and transparent notation that we believe offers new insights. The approach manifests the relationship between the six-vertex and chiral Potts models, and between the eight-vertex and Kashiwara–Miwa models.     

Lattice gas generalization of the hard hexagon model. II. The local densities as elliptic functions

In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.Supported in part by the National Science Foundation Grant MCS 8201733.     

Study of ferromagnetism–superconductivity interactions in Co/Nb multilayers

We investigate Co/Nb multilayers to explore the spontaneous π-phase shift between the superconducting (SC) layers, which is attributed for causing the non-monotonic change of the SC transition temperature (T_c) with the ferromagnetic (FM) layer thickness (t_FM) in several FM/SC multilayered systems. The issue of interfacial roughness is also explored by growing Co/Nb multilayers at various sputtering pressures. Transport measurements show a non-monotonic dependence of T_c on t_FM, and this dependence is insensitive to the structural variation present in the samples, as measured by X-ray scattering.     

Hamiltonian limit of the 3D Zamolodchikov model

A two-dimensional quantum Hamiltonian _N,M commuting with the layer-to-layer transfer matrix of the three-dimensional Zamolodchikov model is derived. This Hamiltonian is defined on a lattice ofN×M sites. The special casesN×2, 2×M, and 3×M are studied.This paper is dedicated to Cyril Domb.     

Free energy of the solvable chiral Potts model

Very recently, it has been shown that there are chiralN-state Potts models in statistical mechanics that satisfy the star-triangle relation. Here it is shown that the relation implies that the free energy (and its derivatives) satisfies certain functional relations. These can be used to obtain the free energy: in particular, we expand about the critical case and find that the exponent is 1–2/N.     

A class of interaction-round-a-face models and its equivalence with an ice-type model

A new model (called the Temperley-Lieb interactions model) is introduced, in two-dimensional lattice statistics, on a square lattice . The Temperley-Lieb equivalence of this model to the six-vertex, self-dual Potts, critical hard-hexagons and critical nonintersecting string models is established. A graphical equivalence of this model to the six-vertex model generalizes this equivalence to noncritical cases of the above models. The order parameters of a specialization of this model are studied.     

Solid-phase synthesis of imidazo[4,5-b]pyridin-2-ones and related urea derivatives by cyclative cleavage of a carbamate linkage

A solid-phase synthesis of substituted cyclic urea derivatives as potential heterocyclic library scaffolds is described. 2-Amino-3-nitropyridine is attached to Wang resin via a carbamate linkage. Reduction of the nitro group was achieved with SnCl(2).2H(2)O. Reductive alkylation with a range of substituted benzaldehydes followed by cyclative cleavage afforded a small library of 3-substituted imidazo[4,5-b]pyridine-2-ones in 33-45% yield and 59-88% purity. Subsequently, this methodology was applied to the synthesis of 3-substituted imidazo[4,5-f]quinolin-2-ones.     

Use of biosensors for rapid drug residue analysis without sample deconjugation or clean-up: a possible way forward.

The drug salbutamol (SBL) is a beta-agonist that may be used illegally as an animal growth promoter. SBL is also a good example of a drug which is excreted in the form of glucuronides and sulfates. Such metabolites cause complexities in analysing for the presence of drug residues. In the majority of cases a process of deconjugation and sample clean-up is required prior to analysis. This is both time consuming and causes some loss of accuracy. In this study, the urine of calves treated with SBL orally for 3 d was collected during and after medication. Samples were assayed before and after hydrolysis by two different methods, radioimmunoassay (RIA) and a newly developed biosensor immunoassay (BIA). Some samples were also analysed by GC-MS. The results clearly showed that both screening assays (RIA and BIA) found high concentrations of SBL residues throughout the study. This was especially true in the BIA method. It was also demonstrated that urine sample analysis without the need for deconjugation or clean-up could be achieved. Results obtained by GC-MS tended to be an order of magnitude lower than the corresponding screening test results. This work showed that biosensor based veterinary drug residue testing procedures can be developed which can generate results in real time without the need for time consuming sample preparation.     

An apparatus for the determination of volatile analytes by stopped-flow injection analysis using an integrated fiber optic detector

A new method for the analysis of volatile analytes using a stopped-flow injection system originating from either a gas or liquid phase has been developed. It uses an integrated fiber optic detector which also serves as a reactor. This system combines the advantages of gas diffusion and stopped-flow, making the overall assay very sensitive. Both gas streams and aqueous solutions containing ammonia were analyzed. The limits of detection are 40 ppb for gas phase analysis and 1.0 ppm for aqueous phase analysis.